Study hypothesis: increased DNA damage by PARP inhibition will complement the anti-tumor activity of the immune checkpoint inhibitor, durvalumab. Study status: Ten patients with recurrent NSCLC have been enrolled, including patients previously treated with immunotherapy. Eight patients are evaluable for response. One (13%) partial response has been observed in a patient who had previously progressed on single-agent pembrolizumab. The study is designed to enroll 20 patients initially. If after interim analysis, the median PFS is 3.5 months or less, the study will close to accrual. If PFS is greater than 3.5 months, accrual will continue until 37 patients are enrolled.